Top frame: comparisons of the observational dataset (black points) with the 2D probability histograms of N_H and N(H₂) computed from the reconstruction algorithm (see Sect. 3.8) applied to thesimulations. Bottom frame: fraction of lines of sight (%), and mean value μ and dispersion σ of the logarithm of the molecular fraction computed from the simulated histograms in the regions A, B, C, D, and E defined in Table 1. Numbers correspond to the values of %, μ, and σ. The color code indicates a measure of distance (in arbitrary units) between the observed and simulated values in order to guide the eye. These comparisons are shown in each frame for 15 different simulations with G₀ varying from 0.5 (left panels) to 4 (right panels) and varying from0.5 cm⁻³ (top panels) to 4 cm⁻³ (bottom panels). All other parameters are set to their fiducial values (see Table 2).